Many description logics (DLs) combine knowledge representation on an
abstract, logical level with an interface to 'concrete' domains like
numbers and strings with built-in predicates such as >, +, and
prefix-of. These hybrid DLs have turned out to be useful
in several application areas, such as reasoning about conceptual
database models. We propose to further extend such DLs with key
constraints that allow the expression of statements like 'US
citizens are uniquely identified by their social security number'.
Based on this idea, we introduce a number of natural description
logics and perform a detailed analysis of their decidability and
computational complexity. It turns out that naive extensions with key
constraints easily lead to undecidability, whereas more careful
extensions yield NExpTime-complete DLs for a variety of useful
concrete domains.

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